Stability of 1+1 dimensional causal relativistic viscous hydrodynamics
J. W. Li, Y. G. Ma, G. L. Ma
TL;DR
This paper investigates the stability of 1+1 dimensional causal relativistic viscous hydrodynamics using Israel-Stewart theory, revealing how shear viscosity can mitigate instabilities caused by bulk viscosity near phase transitions.
Contribution
It provides a stability analysis of Israel-Stewart hydrodynamics in 1+1 dimensions, highlighting the stabilizing role of shear viscosity against bulk viscosity-induced instabilities.
Findings
Shear viscosity weakens bulk viscosity-induced instability.
Temperature evolution and bulk pressure ratio are analyzed.
Lyapunov method confirms stability conditions.
Abstract
The stability of the 1+1 dimensional solution of Israel-Stewart theory is investigated. Firstly, the evolution of the temperature and the ratio of the bulk pressure over the equilibrium pressure of the background is explored. Then the stability with linear perturbations is studied by using the Lyapunov direct method. It shows that the shear viscosity may weaken the instability induced by the large peak of bulk viscosity around the phase transition temperature .
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